Sve što rodbina želi jest da na godišnjici svi budemo zdravi, mirni i zajedno.

Sve što is a very common Croatian pattern meaning all that or everything that.

• sve = everything / all
• što = that / what, introducing a relative clause

So Sve što rodbina želi means all that the relatives want.

This is similar to English structures like:

• All that the family wants is...
• Everything the relatives want is...

Because rodbina is grammatically singular, even though it refers to many people.

It is a collective noun meaning relatives / extended family / kin. Croatian treats it as singular, so the verb must also be singular:

• rodbina želi = the relatives want

This is a bit like English the family wants when we treat family as one group.

Not exactly.

Rodbina usually means relatives, especially the wider family network: aunts, uncles, cousins, in-laws, and so on. It is broader and a bit less intimate than immediate family.

So:

• obitelj = family, often the close family unit
• rodbina = relatives / extended family

In this sentence, rodbina suggests the wider family group.

Jest is the full, stressed form of je.

Both can mean is, but:

• je is the usual short everyday form
• jest sounds more formal, careful, or slightly emphatic

So:

• Sve što rodbina želi je da...
• Sve što rodbina želi jest da...

Both are possible, but jest feels a bit more formal or literary here.

Here da introduces a clause that expresses what is wanted.

Croatian often uses da + finite verb where English might use:

• that...
• for us to...
• or sometimes an infinitive

So jest da... here means something like:

• is that...
• is for us to...

In this sentence, the wanted thing is a whole clause: that we all be healthy, calm, and together at the anniversary.

After da, Croatian often uses budem, budeš, bude, budemo... when talking about a desired, expected, or future-oriented state.

So:

• da budemo zdravi = that we be healthy / that we are healthy in the hoped-for situation

Using smo here would not sound natural in standard Croatian for this meaning. Budemo fits the idea of a wish or desired situation at the time of the anniversary.

So the pattern is:

• želim da budemo... = I want us to be...
• žele da budemo... = they want us to be...

Na godišnjici is in the locative singular.

• base form: godišnjica = anniversary
• after na in the sense of at/on an event, Croatian uses the locative
• so: na godišnjici = at the anniversary / at the anniversary celebration

The ending -i shows the locative singular of this feminine noun.

Also, na is natural here because Croatian often uses na with events and gatherings:

• na sastanku = at the meeting
• na svadbi = at the wedding
• na godišnjici = at the anniversary

Because they are different words with different jobs.

• sve = everything / all that
• svi = everyone / all

So:

• Sve što rodbina želi = all that the relatives want
• da svi budemo... = that we all be...

They look similar, but they are not repeating the same meaning.

They agree with svi, which refers to all of us / everyone.

In Croatian, when a group is mixed or unspecified, the masculine plural is the default form. That is why we get:

• svi budemo zdravi, mirni...

If the whole group were known to be female, you could get feminine plural forms instead:

• sve budemo zdrave, mirne...

But with a general mixed group, masculine plural is normal.

Because zajedno is an adverb, not an adjective.

• zdravi and mirni are adjectives, so they agree with the subject
• zajedno means together, and adverbs do not change for gender, number, or case

So:

• zdravi = healthy
• mirni = calm / peaceful
• zajedno = together

That is why zajedno stays the same.

Yes. Croatian word order is fairly flexible.

For example, you could also say:

• Sve što rodbina želi je da svi na godišnjici budemo zdravi, mirni i zajedno.

That would still be natural.

The original order:

• ...da na godišnjici svi budemo...

slightly brings the anniversary occasion forward. Croatian often moves elements around to shift emphasis, while the meaning stays basically the same.

Because da budemo zdravi, mirni i zajedno is a tightly connected content clause completing the meaning of the sentence.

Croatian normally does not use a comma before da in clauses like:

• Mislim da... = I think that...
• Želim da... = I want that...
• Važno je da... = It is important that...

This sentence follows the same pattern:

• Sve što rodbina želi jest da...

So no comma is needed.